Is there a way of removing and cleaning my fuel injector on a 5.9

 

Yeah, they come out fairly easy, but, you need some fairly specialized equipment to clean 'em. You could probably make something up...... if you have the skills/stuff layin' about. Or, you could send them out to have them cleaned/flow matched, or, you could just replace them.

 

Would I have to remove the fuel rail

 

Yes. The fuel rail holds the injectors down from the top, as the rails are bolted to the intake manifold.

 

Make sure you clean all the dirt/debris away from them, If not it will fall into the injector hole.